Inventory Management

Inventory Management Inventory: A quantity of goods/materials in

the control of a firm and hold for a time in a relatively idle state awaiting its intend use or sale

Inventory Management: To determine an optimal level of holding such idle resources through certain procedures/rules on the decisions of when/how much to order for procurement or production

How How Much?Much? When!When!

Conflicting Pressures on Inventory Levels

Pressures for Small Inventories Pressures for Large Inventories

Interest or opportunity cost Customer service

Storage and handling cost Ordering or setup cost

Property taxes Labor and facility utilization

Insurance premiums Transportation cost

Shrinkage costs: pilferage, obsolescence, and deterioration

Cost of purchased items

Inventory Management (II) Major objectives of inventory

management:

1. Minimizing total inventory management cost under given constraints

2. Satisfying desired customer service level

Functions of Inventory 1. To prevent fluctuation in demand 2. To meet seasonal demand change 3. To protect variation in supply 4. To obtain economy of scale in

procurement/production 5. To maintain independence of operations 6. To smooth production process 7. To provide flexibility for production planning

and scheduling

Type of InventoryInventory types: 1. RM/purchased parts/subassemblies 2. Work-in-process 3. Finished goods

Inventory: Purpose and TypesPurpose: Buffering against any uncertainty in the work flow process from material

purchasing to finished goods shipping through providing a buffer between successive work flow stages.

Types:

Operation Type Inventory Type Buffered Flows

Manufacturing Purchased RMs and Parts

Between Purchasing and manufacturing operations

Work-In-Process Between Successive Production Operations

Finished Goods Between production and Sales

Services Delivery: Supplies Between Purchasing and Services delivery

Wholesale/ Retail Finished goods Stock Between Distribution and Final Sales

Costs Constraints and Customer Service

Relevant costs in inventory management: 1. Fixed costs: purchase ordering

cost/production setup cost 2. Variable costs: holding cost/shortage

cost/purchase costMajor constraint in inventory management: 1. Supply constraint 2. Internal constraint 3. Marketing constraint

Inventory ManagementCosts affected by inventory decisions

Ordering (or setup costs)Clerical costsTransportation and receiving costsCost incurred in setting up

productionOrder follow-up cost

Inventory holding costSpace costsStorage costsCost of capital investedInsurance costsTaxes on investment valuesCosts of spoilage

Stockout or shortage costsExpediting costsRush shipment costsPossible lossLoss of profitPotential loss of customer

Costs of purchased items on which price discounts are offered based on

Total dollar values of purchase order for items

Inventory CostsInventory Costs Interest or opportunity CostInterest or opportunity Cost

Storage and Handling CostsStorage and Handling Costs

Taxes, Insurance, and ShrinkageTaxes, Insurance, and Shrinkage

Customer Service CostCustomer Service Cost

Ordering Cost/Setup CostOrdering Cost/Setup Cost

Labor and Equipment Cost Labor and Equipment Cost

Transportation CostsTransportation Costs

Payments to SuppliersPayments to Suppliers

Customer Service in Inventory Management

Customer Service: measured by the availability of items when needed a performance measure of inventory management

Customer may be: purchaser of FG/distribution/another plant or shop where next operation is performed

Customer Service Level: a target level for keeping initial delivery schedules and backorders

Service Level and Safety Stock Service level: an inventory management

performance criterion measured by

---the percentage of stock-out occurrence defined as service level=1-P(percentage of stock-out)

Safety stock: a quantity of inventory which have been set aside to reduce the probability of stock-out or to improve the service level.

Service Level and Safety StockSafety Stock is: A Quantity of Inventory which have

been set aside to reduce the Probability of Stock-Out, or to improve the Service Level.

The General Relationship Between Safety Stock and Services Level is:

The ABC Classification Method A small percentage of the items that would account for a large percent of the

total values of annual usage- these are called “A” items A large percentage of the item that would account for a small percentage of

the total value of annual usage- these are called “C” items Items in between “A” and “C” items- these are called “B” itemsA typical relationship among A, B and C items is:

ABC AnalysisABC Analysis

1010 2020 3030 4040 5050 6060 7070 8080 9090 100100

Percentage of itemsPercentage of items

Per

cen

tag

e o

f d

oll

ar v

alu

eP

erce

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of

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ue

100 100 —

90 90 —

80 80 —

70 70 —

60 60 —

50 50 —

40 40 —

30 30 —

20 20 —

10 10 —

0 0 —

Figure 15.2Figure 15.2

Class C

Class A

Class B

See ABC Classification Example on your

Supplement (p.15-8)

Reading Article about 80/20 Rule on p. 15-11.

ABC Classification ExamplesA wholesaler has ten items in a product line. The item number, selling price, and estimated annual volume in units are:

item Selling price Annual usage in units

Annual Usage in Values

1001 $3.00 10,000 30,0003080 15.00 350 5,2500053 4.60 4,000 18,4004197 2.56 5,000 12,8003683 21.00 200 4,2004421 0.65 10,500 6,8252222 4.49 12,500 56,1255376 6.38 4,400 28,0722121 4.21 750 3,157.50070 5.44 2,000 10,880

Total= 175,709.50

The first step in categorizing the item is to estimate the dollar value of annual usage for each item (multiply the selling price by the estimated annual usage). Then, they should be arranged in descending order. The result of these two steps are:

Item Value of annual usage

Cumulative value of annual usage

Cumulative percent of value of annual usage

2222 $56,125.00 $ 56,125.00 31.9 %

1001 30,000.00 86,125.00 49.0 A5376 28,072.00 114,197.00 65.0

0053 18,400.00 132,597.00 75.5

4197 12,800.00 145,397.00 82.7

0070 10,880.00 156,277.00 88.9 B

4421 6,825.00 163,352.00 92.8

3080 5,250.00 168,352.00 95.8 C3683 4,200.00 172,552.00 98.2

2121 3,157.50 175,709.50 100.0

Assume the wholesaler wants to construct the ABC classification Assume the wholesaler wants to construct the ABC classification with “A” items representing 75% of the sales, “B” using the table with “A” items representing 75% of the sales, “B” using the table above the classification would be:above the classification would be:

Item A Item B Item C

2222 4197 4421

1001 0070 3080

5376 3683

0053 2121

Classification of Inventory Control Models

Demand Characteristics:1. Independent Demand Item (finished goods):

demand of an item is independent to others usually with high uncertainty uncontrollable and external determined

2. Dependent Demand Item (RM/part/ subassembly): demand of an item is dependent on other items’ requirements usually with certainty controllable and internal determined

Types of Demand Independent Demand

When item’s demand is influenced by market conditions and is not related to (i.e. “independent” of) production decisions for any other item

Only end items can qualify in manufacturing Demand must be forecast (uncontrollable)

Dependent Demand When item’s demand derives from (i.e. “depends” on) the production

decisions for its parent All intermediate and purchased items in manufacturing Demand should be derived (can be controlled)

Some items can be viewed as both “independent” and “dependent” demand items!

Classification of Inventory Control Models

Single item inventory vs. multiple-item inventory

Single stage inventory vs. multi-stage Static demand vs. dynamic demand Stochastic demand vs. determined demand

Five Types of Inventory Control System for Independent Demand Items

1. Fixed Order Quantity (Q)- Reorder Point (R) System: (Q,R) Continue review on inventory status (It),

2. Fixed Order Interval (T)- Maximum Level (M) System: (T,M) Periodical review at fixed time interval (T) Place an order at end of each period with a quantity that build On- Hand Inventory

up to M

3. Hybrid System: Combination of Fixed Order Interval (T) and Reorder Point System (R) (Several Possible Combinations).

4. Time-Phased Order Point System: (MRP Application on Independent Demand Items)

5. Single-Period Model: for Perishable Items (Newspaper/ Flower)

Basic Fixed-Order Quantity Model

Economic Order QuantityEconomic Order Quantity

Figure 15.3Figure 15.3

Inventory depletion Inventory depletion (demand rate)(demand rate)

Receive Receive orderorder

1 cycle1 cycle

On

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d i

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un

its)

On

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d i

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un

its)

TimeTime

QQ

AverageAveragecyclecycleinventoryinventory

QQ——22

Fixed-Interval Inventory System(T,M) System

Continuous ReviewContinuous Review So

up Sou

pS

ou

p

Figure 15.7Figure 15.7

TimeTime

On

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and

in

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tory

RR

TBOTBO

LL

TBOTBO

LL

TBOTBO

LL

OrderOrderreceivedreceived

OrderOrderreceivedreceived

QQ

OHOH

OrderOrderplacedplaced

IPIP

OrderOrderreceivedreceived

QQ

OHOH

OrderOrderplacedplaced

IPIP

OrderOrderreceivedreceived

OrderOrderplacedplaced

IPIP

QQ

OHOH

Periodic Review SystemsPeriodic Review Systems

Figure 15.12Figure 15.12

PP PPTimeTime

On

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and

in

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tory

TT

QQ11

OrderOrderplacedplaced

LL

OrderOrderplacedplaced

OrderOrderreceivedreceived

OrderOrderreceivedreceived

OrderOrderplacedplaced

QQ22

QQ33

OrderOrderreceivedreceived

OHOH

LL LL

Protection intervalProtection interval

IPIP11

IPIP33

IPIP22

IPIP IPIPIPIP

OHOH

Fixed Order Quantity SystemA perceptual system (sometimes called a fixed

quantity or Q/R system) is one that used a fixed reorder point (R) and a fixed order quantity (Q). The time between orders varies depending on when the inventory reaches the reorder point.

Fixed Order Quantity System The inventory behavior is:

LT LT LT

Q QR

(d)

SS= 0

Fixed Order Quantity SystemWhere:

R= reorder point = (d*L) + SS

Q= economic order quantity = EOQ = √D= annual demand (expressed in units/ year)L= reorder lead time (expressed as a fraction of a year)S= ordering cost (expressed as $ per order)C= item cost (expressed in $ per unit)F= inventory holding cost fraction (expressed as a fraction of item cost per year)H= holding cost = (C*F)

The total annual cost (TC) for a purchased item managed with a perpetual inventory system can be calculated as follows:TC= (cost of the item) + (ordering cost) + (inventory holding cost)D*C + ( Q/2)*H + (D/Q)*S

2* DS

H

Example 15.2Example 15.2

3000 3000 —

2000 2000 —

1000 1000 —

0 0 —| | | | | | | |

5050 100100 150150 200200 250250 300300 350350 400400

Lot Size (Lot Size (QQ))

An

nu

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(d

oll

ars)

An

nu

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ost

(d

oll

ars) Total cost = (Total cost = (HH) + () + (SS))

DDQQ

QQ22

Holding cost = (Holding cost = (HH))QQ22

Ordering cost = (Ordering cost = (SS))DDQQ

Economic Order QuantityEconomic Order Quantity

Economic Order QuantityEconomic Order QuantityA

nn

ual

co

st

(do

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)A

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)

Lot Size (Lot Size (QQ))Figure 15.4Figure 15.4

Holding cost (Holding cost (HCHC))

Ordering cost (Ordering cost (OCOC))

Total cost = Total cost = HCHC + + OCOC

See Example on Your Supplement

P. 15-15.

Example of Determining Economic Order Quantity

An importer/distributor or toys uses a standard, corrugated cardboard box for shipping orders to customers. These boxes are used at the rate of 120,000 per year. Each box costs $0.30, and the estimated annual holding cost is 60% of the purchase price.

 

It requires 20 minutes (or 0.33 hours) to prepare an order for this item. The wage rate of the inventory and purchasing clerks is $5.00 per hour.

D=120,000; C=0.30; F=0.60; H=0.3x0.6=0.18

 

Problem: Determine how many boxes should be ordered from the supplier each time.

 

Solution: S= (1/3) x $5= $1.65

EOQ= √2.D.S/H = √2x120,000x1.65/0.18

= 1,483

≈1,500

Problem: If lead time is one day and there are 250 working days during the year, what is the reorder point?

Solution: d= 120,000/250= 480, L=1, SS=0

R= d.L + SS= (480X1) + 0 = 480

Problem: What is the total annual cost of this reordering system?

Solution:

TC = D.C + (D/Q).S + (Q/2).H

= (120,000)(0.3) + (120,000/1,483)1.65+(1483/2)X0.18

= $36,267

Economic Order QuantityEconomic Order Quantity

1.1. Demand rate is constantDemand rate is constant2.2. No constraints on lot sizeNo constraints on lot size3.3. Only relevant costs are holding and Only relevant costs are holding and

ordering/setupordering/setup4.4. Decisions for items are independent Decisions for items are independent

from other itemsfrom other items5.5. No uncertainty in lead time or supplyNo uncertainty in lead time or supply6.6. One Time delivery.One Time delivery.

AssumptionsAssumptions

Fixed Order Quantity System with Gradual Replenishment

The inventory behavior is:

Fixed Order Quantity System with Gradual Replenishment

EPQ= economic production quantity = √

WhereD= annual demand (expressed in units/ year)S= ordering cost (expressed as $ per order)C= item cost (expressed in $ per unit)F= inventory holding cost fraction (expressed as a fraction of item cost per year)P= production rate (expressed in units per period)d= usage rate (expressed in units per period)

TC = [D*C] + ( )*S + ( )*H*( )

2*D*S

H

P

P-d

DQ

Q

2

P-d

P

Special Inventory ModelsSpecial Inventory Models

Production Production and demandand demand

Demand Demand onlyonly

TBOTBO

Production quantityProduction quantity

Demand during Demand during production intervalproduction interval

Maximum inventoryMaximum inventory

On

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and

in

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tory QQ

TimeTime

IImaxmax

p – d

Figure E.1Figure E.1

Imax = (p – d) = Q( )Qp

p – dp

See Example on Your Supplement

P. 15-17.

Example of Determining Economic Production Quantity

A manufacturer of steel products uses a large, special bolt as a fastener in all products in a particular product line. The usage rate of this item is 2000 per day. There are 250 working days in the year. It takes 30 minutes to prepare a manufacturing order for this bolt. The clerks make $5.00 per hour. It takes one hour to change the tooling to begin a production run for the bolt. The setup personnel make $9.00 per hour. The production run is 5000 units per day.C=1.30; F=25%; H=(1.3x25%)=0.325; d= 2,000; D=2,000x250=500,000Problem: What is the economic production quantity for this item assuming a manufacturing cost of $1.30 and an annual holding cost of 25% of the manufacturing cost? S: (0.5x5) + (1x9)= $11.50, P=5,000

EPQ= √(2.D.S)x P/H.(P-d) = √(2x500,000x11.50)x5,000/0.325X(5,000-2,000) ≈7,680 

Problem: If lead time is 1.5 days, what is the reorder point?

Solution:

L= 1.5; SS=0

R = d.L +SS

= 2,000X1.5+0

= 3,000

Periodic Systems

Periodic SystemsT= economic order interval = L= reorder lead time (expressed as a fraction of a year)S= ordering cost (expressed as a fraction of a year)D= annual demand (expressed in units/year)C= item cost (expressed in $ per unit)F= inventory holding cost fraction (expressed as a fraction of item

cost per year)Order quantity =

Q= d(L+T) + SS – It

= M- It

(M= (Base-Level) = d(L+T) + SSIt = [On-Hand] + [On-Order] – [Back Order])

See Example on Your Supplement

P. 15-19.

Example of Determining Economic Order Interval

An auto parts store carrier a universal gasoline filter. The store sells 4000 units of this item annually. The cost of this filter from the supply house is $0.50 and the annual holding cost is 20% of the unit value. The cost of preparing a purchase order is $8.00.

D=4,000; C=0.5; F=20%; H=0.5X0.2=0.1

Problem: If the store is open 51 weeks per year, how many weeks should there be between orders?

S=$8.00

T= √2.S/H.D = √2x8/0.1x4,000

=0.2 (Years) x 51

=10.2 (Weeks)

Problems: If the lead time is one week, what is the quantity to be ordered if 110 units are currently on hand at the end of a reorder interval?

D=4,000/51=78, L=1; It=110, SS=0

Q=d(T+L)+SS-It

=78(10.2+1)+0-110≈770Problem: How many orders should be placed each

year?N= 51/10.2 =5 (Orders)

Hybrid SystemA hybrid inventory system has a combination of a

fixed order interval and a fixed reorder point. Examples of hybrid systems are:

Place an order every 4 weeks unless the inventory drops below 100 units. Then, place the order immediately

Place a order every 4 weeks unless the inventory on hand is more than 250 units. Then, wait another week to place the order

Summary Of Basic Inventory Models

Decision Perpetual System (Q,R)

Periodic System (T,M)

When to order

R= d*L + SST= √

How much to order EOQ = √ Q = d* (L+T)+SS - It2*D*S

H

2*S

H*D

√

EPQ= 2DS H

PP-d( )

Inventory Control System Continuous Review (Q,R) System – fixed-order quantity

system for independent demand item: When a withdrawal brings Inventory down to the reorder point

(R), place an order for Q (fixed) units R= average demand during the lead time + safety stock (safety

stock = z* σL)

Periodic Review (P) System – periodic reorder system. Review the inventory every P time periods- place an order (Q)

equal to (T-IP), where T is the target inventory. Here Q varies, and time between orders (TBO) is fixed. Same

four assumptions, but again allow for uncertain demand.

Inventory Control Models ComparisonFixed Order Quantity [Q,R] vs. Fixed Order Periods [T,M]

Fixed Order Quantity Fixed Order Period

Order Quantity Q is fixed (order same) Q is variable (order different)

Order Time Variable, anytime when on-hand reaching R

Fixed at T (period)

Initiated By Event triggered (when I→R)

Time triggered (when t→T)

Control Point Continuous review on inventory

Periodical review only

Operating Cost Very high Low

Implementation Difficult Easy

Data Managing Difficult and time consuming

Easy and simple

Factors to Consider When Determining which System to Use

Factors favoring a Fix-Order Quantity system:

1. high cost items2. items that have high stockout costs3. items that have discount price based on

order quantity4. items that have relatively more irregular

demand patterns

Factors to Consider When Determining which System to Use

Factors favoring a fix Order-Period system:

1. low cost items

2. items that have low stockout costs

3. items that have discount price based on dollar value

4. items that have relatively regular demand patterns

5. items that can be purchased from the same supplier

6. items that their values will change period-by-period

Comparison of Q and P SystemsComparison of Q and P Systems

P SystemsP Systems

Q SystemsQ Systems

Convenient to administerConvenient to administer Orders may be combinedOrders may be combined IP only required at reviewIP only required at review

Individual review frequenciesIndividual review frequencies Possible quantity discountsPossible quantity discounts Lower, less-expensive safety stocksLower, less-expensive safety stocks

Inventory Control System (II) Comparative Advantage of Two Systems

Periodic review system Administration is convenient Standardized routes for transportation systems Easier to combine orders to same supplier May help with price break or paperwork May reduce supplier’s shipping costs

Continuous review system Tailoring Q to costs for each item Easier for quantity discounts or capacity limitations Less safety stock

Hybrid systems Optional replenishment system Base stock system Special case of Q and P system Single- bin system Two- bin system

Basis for Setting the Order Point In the fixed order quantity system, the ordering process is

trigged when the inventory level drops to a critical point the order point

This starts the lead time the item--lead time is the time to complete all activities associated with placing filling and receiving the order.

During the lead time customers continue to draw down the inventory so during this period that the inventory is vulnerable to stock-out ( run out of inventory)

Customer service level is the probability that a stock out will not occur during the lead time (DDLT).

The order point is set based on: the demand during lead time and the desired customer service level

Basis for Setting the Order Point (II) Order point = expected demand + safety stock The amount of safety stock needed is based on

the degree of uncertainty in the DDLT and the customer service level desired

If there is variability in the DDLT the DDLT is expressed as a distribution discrete /continuous DDLT distribution is appropriate when the demand is very high.

Determine R and Safety StockR= Average Demand during Lead-time + Safety Stock

= d*L + SSSS = determined by desired Service Level (%) and Standard

deviation of (d*L)= z* σL

Example: Service Level = 95%, α = 5%, z=1.96; α = 1%, z= 2.33)Given: (d*L)=250, σL=22, α= 1%, z= 2.33

SS= z* σL = 2.33*22 = 51R = (d*L) + SS = 250 + 51 = 301 ≈ 300

Determine R and Safety Stock

R = Average Demand during Lead Time + Safety Stock= d*L + SS

SS = determined by desired Service Level (%) and Standard deviation of (d*L)= z*σL

Example: Service Level = 95%α = 5% z = 1.96α = 1% z = 2.33

Given:(d*L) = 250 σL = 22 α = 1% z = 2.33

SS = z* σL = 2.33*22 = 51

R = (d*L) + SS = 250 +51 = 301 ~300

Reorder Point / Safety StockReorder Point / Safety Stock

Example 15.5Example 15.5

Average Average demand demand

during during lead timelead time

Average demand

during lead time

Cycle-service level = 85%Cycle-service level = 85%

Probability of stockoutProbability of stockout(1.0 – 0.85 = 0.15)(1.0 – 0.85 = 0.15)

zzLL

RR

Safety Stock/R

Safety stock = zL

= 2.33(22) = 51.3= 51 boxes

Reorder point = ADDLT + SS= 250 + 51= 301 boxes

A Quantity Discount ScheduleOrder Quantity Price per Unit

1-99 $ 4.00

100-199 $ 3.50

200 and over $ 3.00

Example: EOQ with Discount Price Given:

D=1000, S=2000, F=20%

Supplier offered a price discount:If the order quantity: Q < 2000; pay ＄ 100/unit

If the order quantity: Q > 2000; pay ＄ 80/unit

What is the most economic order quantity that minimizes the total cost?

Example: EOQ with Discount Price (II) 1. assume you normally order less than

2000, then

H=? Q*= ? TC=? 2. if you order Q=2000 to obtain the

discount price then:

H=? Q*=? TC=?

Savings=

Example: EOQ with Discount Price

Given: D= 10,000 S= $2,000 F= 20%Supplier offered a price discount:

If order quantity: Q≤ 2000 You pay $100/unitIf order quantity: Q> 2000 You pay $80/unit

What is the most economic order quantity that minimize the total cost? Assume you normally order less than 2000,

Then H= C1*F = $100 * 0.20 = $20,

So, Q*= √ = 1,414 (<2,000)

TC= (10,000 *100) + (1414/2)*20 + (10,000/1414)* 2000 = $1,028,284 If you order (just) Q= 2000 to obtain the discount price ($80), Then H= C2*F= $80*0.20 = $16, with Q* = 2,000

TC= (10,000*80)+2000/2*16 + 10,000/2000*2000= 826,000 Savings: 1,028,284-826,000=$202.284

2*10,000*200020

unattainable

unrational

1,414 2,000

TC

Q

P1=100

P2=80

CC for for PP = $4.00 = $4.00CC for for PP = $3.50 = $3.50CC for for PP = $3.00 = $3.00

PDPD for forPP = $4.00 = $4.00 PDPD for for

PP = $3.50 = $3.50 PDPD for forPP = $3.00 = $3.00

Special Inventory ModelsSpecial Inventory ModelsQuantity DiscountsQuantity Discounts

EOQ EOQ 4.004.00

EOQ EOQ 3.503.50

EOQ EOQ 3.003.00

First First price price breakbreak

Second Second price price breakbreak

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Purchase quantity (Purchase quantity (QQ))00 100100 200200 300300

Purchase quantity (Purchase quantity (QQ))00 100100 200200 300300

First price break

Second price break

(a) Total cost curves with purchased materials added(a) Total cost curves with purchased materials added (b) EOQs and price break quantities(b) EOQs and price break quantities

Figure E.3Figure E.3

Sensitivity of EOQ Model to Changes Sensitivity of EOQ Model ( Effect of changes)

Due to “Square-Root” effect, the EOQ model is relatively “insensitive” to small changes from model parameter.

For change in the demand rate (D) or Order Cost (S):

-D (or S) is the numerator, EOQ varies directly as the square root of D (or S)

For Change in the holding cost (h):

-H is in the denominator, so if H decreases, EOQ increases Errors in estimating D, H and S

Errors such as overestimating ordering cost may be offset by other errors such as overestimating holding cost.

The square root also reduces the effect of errors. If one misses a cost or demand estimate by 10%, the effect on total cost is often undetectable